Performance analysis of the parallel acquisition of weak GPS signals

This thesis provides a comprehensive analysis of the acquisition performance of the mobile-embedded Global Positioning System (GPS) receiver. Particular emphasis is given to the analysis of differentially coherent processing techniques and parallel acquisition strategies. New analytical expressions for the distribution of the decision variable of differentially coherent detectors are derived. In addition, new Gaussian approximations are derived and shown to be more accurate than existing approximations. Using these Gaussian approximations it is demonstrated that the traditional noncoherent combining detector is the best choice when the signal to noise ratio is large, but that differentially coherent combining is a superior choice at low signal to noise ratios. An analysis of the effects of carrier Doppler, code Doppler and data modulation on detector performance is also conducted. For the noncoherent combining detector, new expressions are obtained for the mean and worst case power attenuation due to the combined effects of carrier Doppler and data modulation. Approximate expressions are also derived for the differentially coherent combining detector. New expressions are also obtained for the mean and variance of the time to first hit using a Markov chain model and matrix methods. These models permit the use of numerical techniques to determine the optimal choice of receiver parameters for a given performance requirement. Finally the effect of unknown power levels and multi-access interference (MAI) are considered. A novel technique for detecting MAI, referred to as the power level detector, is introduced and its performance analysed. All results are verified by Monte Carlo computer simulation using a simplified signal model. The simulations were implemented on a 100 processor computer cluster